ST theories are realized by an addition of a scalar field into the theory. Historically, the first ST theory was formulated by Brans and Dicke [1]}; their approach was later generalized to include self-interaction potential of the scalar field, yielding the so-called Wagoner parametrization [2]}, [3]}, in which the scalar field enters the action in a non-trivial way: in the most general case, it can be coupled to spacetime curvature, and to the matter fields. Such a way of introducing a new mediator of gravitational interaction results in many changes gravity manifests itself. For example, a non-minimal (anomalous) coupling between the field and matter part of the action can produce a fifth force acting on the test particles, causing them to deviate from geodesics (however, this effect can be hidden by various screening mechanisms, which are for this reason an essential part of extended gravity models [4]}, [5]}, [6]}). On the other hand, scalar field coupled to the curvature acts as an effective gravitational constant, whose value might depend on spacetime position and matter distribution in the Universe (in agreement with Mach's principle).
